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Some algorithms for the solution of the symmetric eigenvalue problem on a multiprocessor electronic computer

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Conclusions

The theoretical problems related to the stability of reflection transformations and the convergence of the conjugate gradient method have been studied in [4, 6] (in the case of the above method of parallel calculation it is not necessary to study them additionally).

Let us note that the effectiveness of parallel calculations depends on both the algorithm under consideration and the MECM architecture. Thus in the case of the reflection method, the Ke will be determined by two factors, i.e. (firstly) by the difficulty of using the matrix symmetry, and (secondly) by the nonuniform utilization of the processors. With such an organization of the calculations, it is possible to increase the overall effectiveness of MECM by either letting the newly available processors of a new problem operate in the multiprocessor mode, or by improving the coefficient of uniform partition of the original information. For the conjugate gradient method the effectiveness factor is fairly high. This conclusion evidently holds for many well-known iteration methods when the original data of the problem are assigned in the way described above.

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Literatire Cited

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Additional information

Translated from Kibernetika, No. 6, pp. 39–44, November–December, 1983.

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Molchanov, I.N., Khimich, A.N. Some algorithms for the solution of the symmetric eigenvalue problem on a multiprocessor electronic computer. Cybern Syst Anal 19, 779–783 (1983). https://doi.org/10.1007/BF01068566

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Keywords

  • Reflection
  • Operating System
  • Artificial Intelligence
  • System Theory
  • Original Data